1. Field of the Invention
The present invention relates to method and apparatus for forming color images on paper with color inks by color printer, color copy machine or the like.
2. Description of the Related Art
In color CRTs (cathode ray tubes), which are widely used for color television sets, computer monitors and the like, color reproduction is made by controlling the luminances of the primary colors of colored light, red (R), green (G), and blue (B), based on the principle of additive color mixture. On the other hand, color reproduction in hard copying such as by color printer or color copy machine is made by controlling reflectances of colored lights with color inks of cyan (C), magenta (M), and yellow (Y), which are complementary colors of the primaries of colored light, based on the principle of subtractive color mixture.
However, the spectral absorption characteristic of a color ink is broad, as shown in FIGS. 15(a), 15(b) and 15(c) which show the spectral absorption characteristics of inks used in a sublimation type thermal transfer printer, and each ink absorbs unnecessary components other than the complementary colors of its reflected light, so that it does not function as an ideal absorption filter. Therefore, processing called color correction is performed to reproduce desired colors.
A method called masking has been employed for color correction in hard copying. Among the masking methods, most often used is a method called linear masking, which determines an ink-density signal (Y, M, C) by applying a linear operation to a primary color density signal (D.sub.R, D.sub.G, D.sub.B), which expresses the densities of complementary colors of a primary color signal (R, G, B), as shown in the following (1). ##EQU1##
The linear masking assumes that the additive law of densities (Lambert-Beer law) holds in color reproduction that uses real inks and that color reproduction is realized by a linear operation in a whole color space. However, it is known that in color reproduction that uses real inks, eg. by a sublimation type thermal transfer printer, the additive and proportional laws do not hold owing to various nonlinear factors such as resublimation of inks and internal reflection of inks.
Therefore, there has been proposed a nonlinear masking method that determines the density signal (Y, M, C) of inks by a high-degree polynomial. Following is the formula for quadratic masking, which is the simplest nonlinear masking. ##EQU2##
The quadratic masking performs color correction by the quadratic equations incorporating nonlinear factors in color reproduction, and the 27 correction coefficients a.sub.0 to a.sub.26 are determined by the least square method with respect to differences of color densities. (See for example, Image processing for color reproduction, Imaging Part 1, Shashin Kogyo Bessatsu).
Further, color reproduction for hard copying has a problem of the reproducible color gamut. The range of densities realized by a color printer is limited to the maximum printing density inherent to each printer and the density of the paper used for reproduction. Owing to this limitation on the printable densities and the existence of unnecessarily absorbed components, the range of reproducible colors is limited, so that the color gamut reproducible by a color printer is generally smaller than that by a CRT, which employs the principle of additive color mixture.
FIG. 16 shows the color gamuts reproducible by a CRT and a color printer in the perceptually uniform CIE L*u*v* color space. FIG. 16 (a) shows the projection of the color reproduction gamuts on the u*v* plane, FIG. 16 (b) shows the projection on the L*u* plane, and FIG. 16 (c) shows the projection on the L*v* plane In FIG. 16, the color reproduction range of a printer is of the printer whose spectral absorption characteristics are shown in FIG. 15, and the color reproduction gamut of a CRT is of a CRT in the NTSC system.
Since the color reproduction gamut of a printer is smaller than that of a CRT in this way, a signal that requests a color outside the color reproduction gamut of a printer is sometimes input to the printer. This case happens when at least one of the density values (Y, M, C) determined by linear masking or nonlinear masking described above is less than the density of the paper or greater than the maximum density of the printer. Prior arts have performed printing for this unreproduceable ink density using limiters that set the density value to the density of the paper if a density less than the density of the paper is requested and sets the value to the density of the maximum density of the printer if a density greater than the maximum density of the printer is requested.
However, since a density signal of inks and colors people perceive are in nonlinear relations, the limiters for an ink-density signal do not provide optimal adjustment. FIG. 17 shows examples of color reproduction when limiters are used for an ink-density signal obtained by a masking operation. In FIG. 17, P.sub.i, i=1, 2, 3, are desired colors indicated by input signals, and Q.sub.i, i=1, 2, 3, are the corresponding colors indicated by the limiters.
Alternatively, there has been proposed a color correction circuit comprising means for performing a primary correction operation for correcting an output signal (ink density signals) to have a proportional relationship with an input signal (primary color density signals), means for performing a secondary correction operation for minimizing a difference between the density of an input image and that of an output image using the least square method and means for selecting the result obtained by the secondary correction operation if a difference between the result and the input signal is smaller than a predetermined value and, if not, the result obtained by the primary correction operation (See JP-A SHO 63-151263).
Also, there has been proposed a color image processing apparatus in which there is provided a look-up table storing data for judging whether or not an input signal is within the color gamut reproducible by the output apparatus and, if judged that the input signal is within the color gamut, by referring to the look-up table, outputs from a density conversion table are selected and, if judged that it is out of the color gamut, outputs from logarithmic conversion circuit and masking circuit (See JP-A HEI 4-181870).
Thus, according to these prior arts, the ink density signals are determined by a masking operation when the input signal is out of the color gamut reproducible by a printer.
However, since the color gamut of the input signal is wider than that reproducible by a printer, results obtained by masking operation to the input signal out of the color reproduction gamut of the printer contains ink density signals impossible to reproduce by the printer and, therefore, necessitating to subject them to limiting operation.
It is considerable to set correction coefficients for the masking operation so that the ink density signals reproducible by the printer may be obtained even to the input signal out of the color gamut reproducible by the printer. However, in this method, a very large compression of a color space is performed by the masking operation and, therefore, color reproduction may be made using colors very different from input colors resulting in an unnatural color reproduction.
As shown in the above examples, when desired colors corresponding to an input color signal are outside the color gamut reproducible by a printer, prior arts sometimes perform color reproduction using greatly different colors from the ones that people feel to be better, even the better colors exist within the color gamut reproducible by the printer.